Chaotic Dynamics of Structural Members Under Regular Periodic and White Noise Excitations View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017-04-12

AUTHORS

J. Awrejcewicz , A. V. Krysko , I. V. Papkova , N. P. Erofeev , V. A. Krysko

ABSTRACT

In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton’s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity.The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincaré maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed.In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics. More... »

PAGES

25-32

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-57099-0_3

DOI

http://dx.doi.org/10.1007/978-3-319-57099-0_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1084756681


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Institute of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524, Warsaw, Poland", 
          "id": "http://www.grid.ac/institutes/grid.1035.7", 
          "name": [
            "Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Str., 90-924, Lodz, Poland", 
            "Institute of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524, Warsaw, Poland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Awrejcewicz", 
        "givenName": "J.", 
        "id": "sg:person.012103132446.89", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012103132446.89"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050, Tomsk, Russian Federation", 
          "id": "http://www.grid.ac/institutes/grid.27736.37", 
          "name": [
            "Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation", 
            "Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050, Tomsk, Russian Federation"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Krysko", 
        "givenName": "A. V.", 
        "id": "sg:person.016017316223.58", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016017316223.58"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation", 
          "id": "http://www.grid.ac/institutes/grid.78837.33", 
          "name": [
            "Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Papkova", 
        "givenName": "I. V.", 
        "id": "sg:person.010261455615.35", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010261455615.35"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation", 
          "id": "http://www.grid.ac/institutes/grid.78837.33", 
          "name": [
            "Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Erofeev", 
        "givenName": "N. P.", 
        "id": "sg:person.011364225506.66", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011364225506.66"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation", 
          "id": "http://www.grid.ac/institutes/grid.78837.33", 
          "name": [
            "Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Krysko", 
        "givenName": "V. A.", 
        "id": "sg:person.015167266033.92", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015167266033.92"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2017-04-12", 
    "datePublishedReg": "2017-04-12", 
    "description": "In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton\u2019s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity.The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincar\u00e9 maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed.In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics.", 
    "editor": [
      {
        "familyName": "Dimov", 
        "givenName": "Ivan", 
        "type": "Person"
      }, 
      {
        "familyName": "Farag\u00f3", 
        "givenName": "Istv\u00e1n", 
        "type": "Person"
      }, 
      {
        "familyName": "Vulkov", 
        "givenName": "Lubin", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-57099-0_3", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-319-57098-3", 
        "978-3-319-57099-0"
      ], 
      "name": "Numerical Analysis and Its Applications", 
      "type": "Book"
    }, 
    "keywords": [
      "transversal harmonic load", 
      "order Runge-Kutta method", 
      "finite difference method", 
      "numerical results", 
      "structural members", 
      "second-order accuracy", 
      "non-linear phenomena", 
      "Hamilton's variational principle", 
      "Timoshenko hypotheses", 
      "harmonic load", 
      "beam vibration", 
      "vibration type", 
      "Runge-Kutta method", 
      "boundary conditions", 
      "difference method", 
      "harmonic excitation", 
      "finite differences", 
      "variational principle", 
      "Ruelle-Takens", 
      "white Gaussian noise", 
      "analysed beam", 
      "white noise excitation", 
      "Newhouse scenario", 
      "additive white Gaussian noise", 
      "beam dynamics", 
      "Poincar\u00e9 map", 
      "noise excitation", 
      "Gaussian noise", 
      "noise action", 
      "power spectrum", 
      "vibration", 
      "noise", 
      "load", 
      "phase portraits", 
      "non-linear dynamical systems", 
      "beam", 
      "theoretical background", 
      "time series", 
      "Lyapunov exponents", 
      "dynamics", 
      "method", 
      "white noise intensity", 
      "excitation", 
      "accuracy", 
      "Periodic", 
      "noise intensity", 
      "chaotic dynamics", 
      "results", 
      "dynamical systems", 
      "amplitude", 
      "conditions", 
      "phenomenon", 
      "work", 
      "exponent", 
      "system", 
      "PDE", 
      "route", 
      "scenarios", 
      "frequency", 
      "principles", 
      "means", 
      "help", 
      "transition", 
      "maps", 
      "ODEs", 
      "intensity", 
      "analysis", 
      "types", 
      "series", 
      "spectra", 
      "partition", 
      "charts", 
      "cases", 
      "study", 
      "nodes", 
      "differences", 
      "action", 
      "portrait", 
      "background", 
      "members", 
      "hypothesis", 
      "uniform transversal harmonic load", 
      "beam partition", 
      "beam vibration types", 
      "different wavelet-based studies", 
      "wavelet-based studies", 
      "novel non-linear phenomena", 
      "chaotic beam vibrations", 
      "additive white noise action", 
      "white noise action", 
      "Regular Periodic"
    ], 
    "name": "Chaotic Dynamics of Structural Members Under Regular Periodic and White Noise Excitations", 
    "pagination": "25-32", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1084756681"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-57099-0_3"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-57099-0_3", 
      "https://app.dimensions.ai/details/publication/pub.1084756681"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-01-01T19:20", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/chapter/chapter_339.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-319-57099-0_3"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57099-0_3'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57099-0_3'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57099-0_3'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-57099-0_3'


 

This table displays all metadata directly associated to this object as RDF triples.

197 TRIPLES      23 PREDICATES      116 URIs      109 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-57099-0_3 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N49a7e49ffeaf46b3aabe98286f96285c
4 schema:datePublished 2017-04-12
5 schema:datePublishedReg 2017-04-12
6 schema:description In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton’s variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity.The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincaré maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed.In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics.
7 schema:editor N182a41993d194b9980a691fd19765497
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf Ne67afd10652f4ee2b813897579ed4a03
12 schema:keywords Gaussian noise
13 Hamilton's variational principle
14 Lyapunov exponents
15 Newhouse scenario
16 ODEs
17 PDE
18 Periodic
19 Poincaré map
20 Regular Periodic
21 Ruelle-Takens
22 Runge-Kutta method
23 Timoshenko hypotheses
24 accuracy
25 action
26 additive white Gaussian noise
27 additive white noise action
28 amplitude
29 analysed beam
30 analysis
31 background
32 beam
33 beam dynamics
34 beam partition
35 beam vibration
36 beam vibration types
37 boundary conditions
38 cases
39 chaotic beam vibrations
40 chaotic dynamics
41 charts
42 conditions
43 difference method
44 differences
45 different wavelet-based studies
46 dynamical systems
47 dynamics
48 excitation
49 exponent
50 finite difference method
51 finite differences
52 frequency
53 harmonic excitation
54 harmonic load
55 help
56 hypothesis
57 intensity
58 load
59 maps
60 means
61 members
62 method
63 nodes
64 noise
65 noise action
66 noise excitation
67 noise intensity
68 non-linear dynamical systems
69 non-linear phenomena
70 novel non-linear phenomena
71 numerical results
72 order Runge-Kutta method
73 partition
74 phase portraits
75 phenomenon
76 portrait
77 power spectrum
78 principles
79 results
80 route
81 scenarios
82 second-order accuracy
83 series
84 spectra
85 structural members
86 study
87 system
88 theoretical background
89 time series
90 transition
91 transversal harmonic load
92 types
93 uniform transversal harmonic load
94 variational principle
95 vibration
96 vibration type
97 wavelet-based studies
98 white Gaussian noise
99 white noise action
100 white noise excitation
101 white noise intensity
102 work
103 schema:name Chaotic Dynamics of Structural Members Under Regular Periodic and White Noise Excitations
104 schema:pagination 25-32
105 schema:productId N83e16b37237f4f0c8218050555b582ce
106 Ned105ccccc0a441eac74ea51271ac890
107 schema:publisher N072e81af0a0a42febb36ea852b497a8a
108 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084756681
109 https://doi.org/10.1007/978-3-319-57099-0_3
110 schema:sdDatePublished 2022-01-01T19:20
111 schema:sdLicense https://scigraph.springernature.com/explorer/license/
112 schema:sdPublisher N135160b5f3ca4059923e02e28f3d0767
113 schema:url https://doi.org/10.1007/978-3-319-57099-0_3
114 sgo:license sg:explorer/license/
115 sgo:sdDataset chapters
116 rdf:type schema:Chapter
117 N072e81af0a0a42febb36ea852b497a8a schema:name Springer Nature
118 rdf:type schema:Organisation
119 N097a48af0ae64580894751d8f64dd5ea rdf:first sg:person.016017316223.58
120 rdf:rest N3316e9538d6045b3a7d96ddd305d5a9f
121 N0dffe2884a314410b9c61d39b9abaeae schema:familyName Vulkov
122 schema:givenName Lubin
123 rdf:type schema:Person
124 N135160b5f3ca4059923e02e28f3d0767 schema:name Springer Nature - SN SciGraph project
125 rdf:type schema:Organization
126 N182a41993d194b9980a691fd19765497 rdf:first Nc94be449788b45ad8812e6353013c34e
127 rdf:rest N3430d875a9504f5a96c7baa9f2188c6a
128 N297d80eaacff449aae74d947f935c068 rdf:first sg:person.011364225506.66
129 rdf:rest Nd5dbebaf07b74e40808ed50674fb4ec6
130 N3316e9538d6045b3a7d96ddd305d5a9f rdf:first sg:person.010261455615.35
131 rdf:rest N297d80eaacff449aae74d947f935c068
132 N3430d875a9504f5a96c7baa9f2188c6a rdf:first Ne8acc61c7c82425692adb1f2869d4897
133 rdf:rest N9fb6bf07d4ed489fa8531a89940c3108
134 N49a7e49ffeaf46b3aabe98286f96285c rdf:first sg:person.012103132446.89
135 rdf:rest N097a48af0ae64580894751d8f64dd5ea
136 N83e16b37237f4f0c8218050555b582ce schema:name doi
137 schema:value 10.1007/978-3-319-57099-0_3
138 rdf:type schema:PropertyValue
139 N9fb6bf07d4ed489fa8531a89940c3108 rdf:first N0dffe2884a314410b9c61d39b9abaeae
140 rdf:rest rdf:nil
141 Nc94be449788b45ad8812e6353013c34e schema:familyName Dimov
142 schema:givenName Ivan
143 rdf:type schema:Person
144 Nd5dbebaf07b74e40808ed50674fb4ec6 rdf:first sg:person.015167266033.92
145 rdf:rest rdf:nil
146 Ne67afd10652f4ee2b813897579ed4a03 schema:isbn 978-3-319-57098-3
147 978-3-319-57099-0
148 schema:name Numerical Analysis and Its Applications
149 rdf:type schema:Book
150 Ne8acc61c7c82425692adb1f2869d4897 schema:familyName Faragó
151 schema:givenName István
152 rdf:type schema:Person
153 Ned105ccccc0a441eac74ea51271ac890 schema:name dimensions_id
154 schema:value pub.1084756681
155 rdf:type schema:PropertyValue
156 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
157 schema:name Mathematical Sciences
158 rdf:type schema:DefinedTerm
159 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
160 schema:name Pure Mathematics
161 rdf:type schema:DefinedTerm
162 sg:person.010261455615.35 schema:affiliation grid-institutes:grid.78837.33
163 schema:familyName Papkova
164 schema:givenName I. V.
165 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010261455615.35
166 rdf:type schema:Person
167 sg:person.011364225506.66 schema:affiliation grid-institutes:grid.78837.33
168 schema:familyName Erofeev
169 schema:givenName N. P.
170 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011364225506.66
171 rdf:type schema:Person
172 sg:person.012103132446.89 schema:affiliation grid-institutes:grid.1035.7
173 schema:familyName Awrejcewicz
174 schema:givenName J.
175 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012103132446.89
176 rdf:type schema:Person
177 sg:person.015167266033.92 schema:affiliation grid-institutes:grid.78837.33
178 schema:familyName Krysko
179 schema:givenName V. A.
180 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015167266033.92
181 rdf:type schema:Person
182 sg:person.016017316223.58 schema:affiliation grid-institutes:grid.27736.37
183 schema:familyName Krysko
184 schema:givenName A. V.
185 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016017316223.58
186 rdf:type schema:Person
187 grid-institutes:grid.1035.7 schema:alternateName Institute of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524, Warsaw, Poland
188 schema:name Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski Str., 90-924, Lodz, Poland
189 Institute of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524, Warsaw, Poland
190 rdf:type schema:Organization
191 grid-institutes:grid.27736.37 schema:alternateName Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050, Tomsk, Russian Federation
192 schema:name Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050, Tomsk, Russian Federation
193 Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation
194 rdf:type schema:Organization
195 grid-institutes:grid.78837.33 schema:alternateName Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation
196 schema:name Department of Mathematics and Modeling, Saratov State Technical University, 77 Politechnicheskaya Str., 410054, Saratov, Russian Federation
197 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...